In the second set of experiments we want to find the smallest eigenvalue of an indefinite matrix. As proved in [1]}, if a matrix \(A\)  has at least one negative eigenvalue, we can use formulation (REF ) with \(b = 0\)  to find the smallest eigenvalue. We compare our two algorithms with the algorithm from [2]} and the power method. We consider matrices \(A\)  from University of Florida Sparse Matrix Collection [3]} and also matrices generated randomly (i.e., \(A = Q^{T}BQ\) , with \(Q\)  orthogonal and \(B \in \mathbb {R}^{n \times n}\)  diagonal). The starting point \(x_{0}\)  was generated from a standard normal distribution \(\mathcal {N}(0,1)\) . Table REF  shows the number of full iterations (ITER), CPU time in seconds (CPU) and the eigenvalue found by each method (EIG). As one can see, RCGD method with \(H_{f,U_{i_k}}= 0.51 \cdot \Vert U^{T}_{k}AU_{k}\Vert \)  has the best performance. Moreover, coordinate descent methods are faster on random data. Finally, Tables REF  and REF  show that coordinate descent methods perform better when the gap \(\lambda _{1}(A) - \lambda _{2}(A)\)  is large.
